I can give you the UK spec, because it's what we do. Webbing for lifting or securing is polyester unless use dictates another material (Chemical applications etc). Thread to be compatible with webbing, so polyester (we use number 12 mostly, google conversion to US size). Sew pattern to be one that doesn't stand proud of webbing excessively (so number one in pic above). Lifting straps have a safety factor of 7~1 (so a 1 ton lifting strap will exceed 7 tons before breaking). Load securing straps 2~1 safety factor. Lifting straps above 1 inch to have either single or double becketted eyes. Batch numbers of webbing to be recorded along with strap ID number, customer, load, length, date of manufacture, type of strap (Endless, simplex, duplex etc). Straps to be tested when first ones made or method of manufacture changes (stitch pattern or different webbing supplier etc) and periodically thereafter (keep broken ones along with details and test data).
There's probably more but it's late here and I'm tired.